Kinetic gelation model

Kinetic Gelation Modeling of Crosslinked Network Structure.197... 

Kinetic gelation models [178] have been used to determine, within experimental error, the fraction of constrained and unconstrained double bonds over a wide range of conversions in the polymerization of ethylene glycol dimethacrylate. The amount of unconstrained and constrained functional groups was determined experimentally by solid state nuclear magnetic resonance spectroscopy. The rules for determining constraint in the model were that all pendant double bonds and all monomers in pools of six or less are constrained. Monomers in pools of seven or more are assumed to be unconstrained. Whether a site is constrained or not does not affect the reactivity only the analysis of the model is affected by the rules defining constraint. 

Fig. 9. Kinetic gelation model prediction (heterogeneous limit),-, of monomer conversion vs...

Fig. 10. Kinetic gelation model prediction of the relative fraction of crosslinks, primary cycles, and secondary cycles as a function of double bond conversion for the polymerization of a multifunctional monomer...

Despite its limitations, kinetic gelation modeling is still a very useful tool in simulating network structure in highly crosslinked systems. While kinetic gelation models have gained widespread use in the polymer science field, the application of these models to dental materials and their development appears to be an area appropriate for further exploration. 

Mei, W. Me Cormick, A.V. Scriven, L.E. Kinetic gelation modeling structural inhomogeneity during cross-linking polymerization. Macromolecules 2003, 36, 4140. 

ISTS impulsive stimulated thermal scattering KGM kinetic gelation model... 

Kinetic gelation simulations seek to follow the reaction kinetics of monomers and growing chains in space and time using lattice models [43]. In one example, Bowen and Peppas [155] considered homopolymerization of tetrafunctional monomers, decay of initiator molecules, and motion of monomers in the lattice network. Extensive kinetic simulations such as this can provide information on how the structure of the gel and the conversion of monomer change during the course of gelation. Application of this type of model to polyacrylamide gels and comparison to experimental data has not been reported. 

An alternative description of gelation is given by kinetic growth models. These also explain the different microstructures upon changing the reaction conditions. Depending on the conditions, growth in silicate systems may occur predominantly by condensation of clusters with monomers or with other clusters. The rate of the condensation reactions may be diffusion or reaction limited. 

This section treats the basis of the kinetic aspects of gelation models. All the conclusions in the above sections have been drawn from static models, considering the structure only. Now we have to ask how one derives the properties by a proper kinetic model from a rate equation corresponding to a reaction of the general type... 

Torkelson and coworkers [274,275] have developed kinetic models to describe the formation of gels in free-radical pol5nnerization. They have incorporated diffusion limitations into the kinetic coefficient for radical termination and have compared their simulations to experimental results on methyl methacrylate polymerization. A basic kinetic model with initiation, propagation, and termination steps, including the diffusion hmitations, was found to describe the gelation effect, or time for gel formation, of several samples sets of experimental data. 

All models described up to here belong to the class of equilibrium theories. They have the advantage of providing structural information on the material during the liquid-solid transition. Kinetic theories based on Smoluchowski s coagulation equation [45] have recently been applied more and more to describe the kinetics of gelation. The Smoluchowski equation describes the time evolution of the cluster size distribution N(k) ... 

In conclusion, it is now possible to reproduce the kinetic behavior of this sreroid/cyclohexane gelling system, including the shape ( defined by model (3) and its kinetic rate constants k, k, k ) and also the absolute values of C p in zone A of the phase diagram. In Figure 13, we demonstrate the reversibility of the gelation process and the additivitv of p values for different... 

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